Mulhall, Bridget, Head, born December 1839, single, born Ireland, parents b. same, immigrated 1847
The same immigration date shows up in the 1910 census, so would suggest that she came over earlier than you thought and that she would have likely come with her parents, given how young she would have been.
Have you gotten a copy of her death registration which may provide more information. I am unable to find her in Colorado prior to 1900, so wonder where she was before that.
I did find a possible in New Jersey in 1870:
West Hoboken, Hudson County, New Jersey
Mulhall, Briget, aged 30, domestic servant, born Ireland (living and working in home of a French family whose name I cannot make out - the husband is a physician).